Project Summary: Motivated by the need of physicians and patients to make informed decision, probability methods are proposed to address the problem of when to schedule the next exam for an asymptomatic individual with a history of negative screenings. The method provides a screening time interval to limit the risk of being a clinical incident case to a small value, such as 5% or 10%. The time interval is a function of the three key parameters (i.e., screening sensitivity, sojourn time in preclinical state and transition time distribution in disease-free state), a person's current age/gender, smoking status, and one's screening history. Distribution of Lead time (ie. diagnosis time advanced by screening) and probability of over-diagnosis are derived, if one would be diagnosed with cancer at the future scheduled time. A new likelihood function to estimate the three key parameters are proposed and will be validated to increase the accuracy of the estimation. The methods will be applied to four cohorts from the Prostate, Lung, Colorectal, and Ovarian Cancer Screening Trial for lung cancer (PLCO-Lung) and four cohorts from the National Lung Screening Trials (NLST). The specific aims are: 1. To estimate the three key parameters using a new likelihood function in the eight cohorts using either chest X-ray or Low Dose Computed Tomography (CT). Eight cohorts (four from PLCO-Lung using X-ray: male/female smokers, male/female never-smokers; four from NLST: male/female smokers via X-ray, male/female smokers via CT) were identified. The three key parameters will be estimated when sensitivity is modeled as a function of the sojourn time and time spent in the preclinical state using our new likelihood method. This lays a foundation for predictions and estimations in Aim 2, since the future time interval is a function of the three key parameters; and we will plug in estimates of the three key parameters in Aim 2 to obtain the optimal screening time. 2. To schedule the next screening exam dynamically for an asymptomatic individual with any screening history. A new method using conditional probability of incidence before the next exam is proposed. The next screening time is found by limiting this probability to a small value, to guarantee early detection and control the risk of over-diagnosis. The lead-time distribution and the probability of over-diagnosis are derived, if one would be diagnosed with cancer at the next proposed screening time, so that predictive information can be provided to individuals on how early his/her disease could be detected, and the risk of over-diagnosis if one undergoes screening exams as suggested. 3. To develop a user-friendly software for Aims 1 and 2, and made available to the public. In summary policy makers can use information from this research to recommend future screening frequencies for different risk groups (e.g., age, gender, smoking status) under different screening techniques (X-ray or CT). Physicians may use results from Aim 3 (the developed software) to schedule the next exam for individuals.